Please note: io:async is not the same thing as IO::Async -- it would not be able to find the first, but should find the second. To force in that client, cpan -f -i IO::Async (but forcing should be a last resort.)

However, given that Re^4: Unable to install module IO::Async::Loop on windows 10 strawberry Perl lists a successful combination, I'm not sure why you aren't trying that.

Please note: that successful combination used IO::Async v0.78, which was current in 2021. As seen at cpantesters, the current v0.802 doesn't have any passes on mswin32, and max versions with a pass shows that IO::Async last passed on mswin32 with v0.78 -- the same version mentioned elsewhere in this thread. So that means maybe you should try to install an older version of IO::Async rather than the most-recent.

So my recommendation to you, based on that:

• Since you said you have Strawberry 5.28.2, use that version rather than 5.32.2, as that's a "known working" version, based on other statements in this thread (though the max-versions shows 5.32.2 can succeed with IO::Async v0.78 as well)
• Update Socket as vr suggested: cpanm Socket
• Install the specific version of IO::Async v0.78: cpanm IO::Async@0.78

(I used cpanm client instead of cpan because it comes with Strawberry, I know it better, and the syntax for installing a specific revision is natural.)

Caveat: I haven't tried installing this myself. (I would have waited for vr to comment, but since it appears to have been 24 weeks since the last login... I don't think you want to wait...)